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# An urn contains 3 white and 6 red balls. Four balls are drawn one by one with replacement from the urn. Find the probability distribution of the number of red balls drawn. Also, find mean and variance of the distribution.

Given: An urn contains 3 white and 6 red balls

To find: the probability distribution of the number of red balls drawn and mean and variance of the distribution

Let X denote the number of red balls drawn in four balls from total of 9 balls

X can have five value, i.e. 0, 1, 2, 3, 4 as there are 6 red balls

Now,

Probability of getting 0 red ball = P(X=0)

The probability of getting 1 red ball = P(X=1)

The probability of getting 2 red balls = P(X=2)

The probability of getting 3 red balls = P(X=3)

The probability of getting 4 red balls = P(X=4)

Probability Distribution Table

Formula used:

Therefore,

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